Stanford University
Neural Interaction Lab

Research

Researchers have developed efficient, parallelizable methods for computing measure transport maps, leveraging convex optimization and nonequilibrium thermodynamics to address uncertainty in high-dimensional datasets, with applications in Bayesian inference, active learning, probabilistic sleep staging, and generative modeling.

Applied Probability

The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution P to another distribution Q enables the solution to many problems in machine learning and has been actively pursued from theoretical, computational, and application perspectives across the fields of information theory, computer science, and biology. Performing such transformations in general purpose manners still comprises computational difficulties, especially in high dimensions. Recently, we consider the problem of computing such “measure transport maps” with efficient and parallelizable methods. Under very mild assumptions, we provide a convex optimization problem to constructing such maps from only samples of P. We recently have also leveraged findings from nonequilibrium thermodynamics to represent the transport map as a composition of simpler maps, each of which is learned sequentially with another related efficiently solvable convex optimization algorithm. We are currently using this framework within the context of Bayesian inference for uncertainty quantification in biomedical datasets, active learning for human computer interfaces, density estimation for probabilistic sleep staging with EEG, and generative modeling with images.

Publications

Illustration of research area applied probability
Stanford
University

Stanford University. Stanford, California 94305